Optical nonlinear processes are indispensable in a wide range of applications, including ultrafast lasers, microscopy, and quantum information technologies. Among the diverse nonlinear processes, second-order effects usually overwhelm the higher-order ones, except in centrosymmetric systems, where the second-order susceptibility vanishes to allow the use of the third-order nonlinearity. Here we demonstrate a hybrid photonic platform whereby the balance between second- and third-order susceptibilities can be tuned flexibly. By decorating ultra-high-Q silica microcavities with atomically thin tungsten diselenide, we observe cavity-enhanced second-harmonic generation and sum-frequency generation with continuous-wave excitation at a power level of only a few hundred microwatts. We show that the coexistence of second- and third-order nonlinearities in a single device can be achieved by carefully choosing the size and location of the two-dimensional material. Our approach can be generalized to other types of cavities, unlocking the potential of hybrid systems with controlled nonlinear susceptibilities for novel applications.
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